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Working with Probabilities Physics 115a (Slideshow 1) A. Albrecht

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Working with Probabilities Physics 115a (Slideshow 1) A. Albrecht These slides related to Griffiths section 1.3. Consider the following group of people in a room:. Histogram Form. Consider the following group of people in a room:. Total people = 14.

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slide1

Working with Probabilities

Physics 115a (Slideshow 1)

A. Albrecht

These slides related to Griffiths section 1.3

slide17

Assuming no age constraint, what is the probability of finding each age?

Related to collapse of the waveunction (“changing the question”)

Total people = 14

slide18

Assuming Age<20, what is the probability of finding each age?

Related to collapse of the waveunction (“changing the question”)

Total people = 14

slide28

Lessons so far

  • A simple application of probabilities
  • Normalization
  • “Re-Normalization” to answer a different question
  • Adding two “systems”.
  • All of the above are straightforward applications of intuition.
slide30

Most probable answer = 25

Median = 23

Average = 21

slide31

Most probable answer = 25

Median = 23

Average = 21

Lesson: Lots of different types of questions (some quite similar) with different answers. Details depend on the full probability distribution.

slide32

Average (mean):

  • Standard QM notation
  • Called “expectation value”
  • NB in general (including the above) the “expectation value” need not even be possible outcome.
slide34

Careful: In general

In general, the average (or expectation value) of some function f(j) is

slide41

Continuous Variables

Why not measure age in weeks?

slide45

Another case where a measure of age in weeks might by useful:

The ages of students taking health in the 8th grade in a large school district (3000 students).

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